20/04/30 08:06:02.99 uKv4ftJu.net
>>575 追加
David Roberts 氏のカテゴリーを使った議論（有名なｗ「識別の危機」）に対する
Dupuy氏の反論もあるね（＾＾
（参考）
URLﾘﾝｸ(www.math.columbia.edu)
Not Even Wrong
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Posted on April 3, 2020 by woit
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Taylor Dupuy says:
April 29, 2020 at 4:37 pm
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Categorical Structure is Not What Matters
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I will explain why (naked) equivalence of categories is not the appropriate notion to be using to reduce structure in Mochizuki’s proof. The appropriate notion is bi-interpretability.
The idea here is that one needs equivalence of *highly structured categories* and if this notion is not used we lose a lot of information.
David Roberts actually makes this point as well in his Inference essay.
Example. Consider a non CM elliptic curve up to isomorphism (as a relative object). If we were just going to consider it by itself then the connected groupoid of curves determined by this object is equivalent to a category with a single object and two morphisms
(because the automorphism group will be a group of order two)!
A connected groupoid with two morphisms doesn’t allow you to do much.